Best simultaneous approximations, asymptotically nonexpansive mappings and variational inequalities in Banach spaces

A. R. Khan; F. Akbar

doi:10.1016/j.jmaa.2009.01.007

Best simultaneous approximations, asymptotically nonexpansive mappings and variational inequalities in Banach spaces

A. R. Khan^*, F. Akbar

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

The existence of common fixed points is established for three mappings where T is either generalized (f, g)-nonexpansive or asymptotically (f, g)-nonexpansive on a nonempty subset of a Banach space. As applications, the invariant best simultaneous approximation results are proved and the existence of solution of variational inequalities is obtained. Our results unify and substantially improve several recent results existing in the current literature.

Original language	English
Pages (from-to)	469-477
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	354
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2009.01.007
State	Published - 15 Jun 2009

Keywords

Asymptotically (f, g)-nonexpansive maps
Banach operator pair
Best simultaneous approximation
Common fixed point
Variational inequalities

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2009.01.007

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title = "Best simultaneous approximations, asymptotically nonexpansive mappings and variational inequalities in Banach spaces",

abstract = "The existence of common fixed points is established for three mappings where T is either generalized (f, g)-nonexpansive or asymptotically (f, g)-nonexpansive on a nonempty subset of a Banach space. As applications, the invariant best simultaneous approximation results are proved and the existence of solution of variational inequalities is obtained. Our results unify and substantially improve several recent results existing in the current literature.",

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AU - Akbar, F.

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N2 - The existence of common fixed points is established for three mappings where T is either generalized (f, g)-nonexpansive or asymptotically (f, g)-nonexpansive on a nonempty subset of a Banach space. As applications, the invariant best simultaneous approximation results are proved and the existence of solution of variational inequalities is obtained. Our results unify and substantially improve several recent results existing in the current literature.

AB - The existence of common fixed points is established for three mappings where T is either generalized (f, g)-nonexpansive or asymptotically (f, g)-nonexpansive on a nonempty subset of a Banach space. As applications, the invariant best simultaneous approximation results are proved and the existence of solution of variational inequalities is obtained. Our results unify and substantially improve several recent results existing in the current literature.

KW - Asymptotically (f, g)-nonexpansive maps

KW - Banach operator pair

KW - Best simultaneous approximation

KW - Common fixed point

KW - Variational inequalities

UR - https://www.scopus.com/pages/publications/60349094636

U2 - 10.1016/j.jmaa.2009.01.007

DO - 10.1016/j.jmaa.2009.01.007

M3 - Article

AN - SCOPUS:60349094636

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VL - 354

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EP - 477

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Best simultaneous approximations, asymptotically nonexpansive mappings and variational inequalities in Banach spaces

Abstract

Keywords

ASJC Scopus subject areas

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